We study the design of multi-armed parallel group clinical trials to estimate personalized treatment rules that identify the best treatment for a given patient with given covariates. Assuming that the outcomes in each treatment arm are given by a homoscedastic linear model, with possibly different variances between treatment arms, and that the trial subjects form a random sample from an unselected overall population, we optimize the (possibly randomized) treatment allocation allowing the allocation rates to depend on the covariates. We find that, for the case of two treatments, the approximately optimal allocation rule does not depend on the value of the covariates but only on the variances of the responses. In contrast, for the case of three treatments or more, the optimal treatment allocation does depend on the values of the covariates as well as the true regression coefficients. The methods are illustrated with a recently published dietary clinical trial.

翻译：我们研究多武装平行小组临床试验的设计,以估计个人化治疗规则,确定对特定病人的最佳治疗方法,并给定共变体。假设每个治疗臂的结果都由同质线性模型给出,治疗臂之间可能存在差异,试验对象从未选定的总人口中随机抽取样本,我们优化(可能随机)治疗分配,使分配率取决于共变体。我们发现,就两种治疗而言,大约最佳分配规则并不取决于共变体的价值,而只取决于反应的差异。相比之下,对于三种或三种以上治疗,最佳治疗分配取决于共变体的价值以及真正的回归系数。最近公布的饮食临床试验说明了这些方法。